"Dvoretsky's Endgame Manual" is exactly one such book that contains a lot of these short facts. You can treat it similarly to an encyclopedia in that regard. Throughout, he writes these key tidbits of advice in italics like so:


I will caution you though that the actual meat of this book is incredibly involved and is most appropriate for players >2000 OTB. There are other books out there that contain the most simplified bits of advice. Shameless plug for my own set of lichess studies on the endgame that contains exactly those bits of info that I think are most relevant without the most complicated examples. I've linked to the study for advanced players, but there are also studies for beginners, studies for intermediate players, and studies specific to rook endgames linked throughout. I describe the "rules" of king and pawn endgame races as follows:

Finally I can address your exact question. The endgame is the portion of the game where one must calculate the most precisely. These general rules are helpful to help guide one's thoughts, but remember: nothing beats a good move. There are countless counterexamples to the general principles. Without an endgame manual or similar to show you how and why the general facts/rules work and fail, the rules are not so useful on their own. So yes you should necessarily go through guided material that presents the rules. No you should not just read the rules by themselves.